Other realms as in parallel universes? Some believe that at every possible choice, a fork happens in theoretical universes, in which both things occur.
If such a thing is ever proven real, we do not yet have the ability to observe or visit.
Other as in physical versus spiritual planes? Earth, Heaven and Hell? Physical, Astral, Ethereal, and Afterlife? There are as many lists as there are beliefs. All of these are a matter of belief, rather than fact. Are they real? In the mind of the observer, they might be. But it does not prove or disprove them.
Can people visit them? Again, it is a matter of belief, as spiritual journeying (all of the various types) are a thing believed, but not provable.
This is indeed a tricky question to answer. For those who have practiced reaching out to other realms/planes and have seen some form of success, they exist. Usually on an alternate energy level such as through the astral. ...Somewhere that might be reached through a conscious shift of awareness but not through a physical means.
For those who haven't, having tried to or not, such places do not exist. This is for simple reason that without evidence there is no proof. And in subgective matters like tbis experience is the best evidence.
Even in scientific study the question stubbornly persists. Modern experiments, theories,and discoveries have ydt to prove such things exist yet some things allude very stongly to the possibility it does.
I suppose in the end I would referr to it being a measure of probability. Like Schroedinger's cat it both does and doesn't exist. For those who have had experiences, they probably exist in some form even if they can't be proven real. For those without experiences they probably don't exist because they can't be proven real. Either way each individual needs to find their own answer.
In all honesty though I don't think it terribly matters either way. At least when compared to a more relevant question; Does believing other realms exist have value? IE: Would gaining experiences around other realms or planes provide you with learning and growth that would help you improve yourself as a person in the here and now? Or is the search an attempt to escape the here and now?
Most often that is a more pertinant question for any individual to explore. And the answsr you find for yourself will tell you if reaching for the possibilities will have value to you. If you have your feet on the ground it can be a powerful tool for Self exploration and growth. If not then it is just as likely to become a roadblock.